Ultrasonic Imaging
Ultrasound is an acoustic signal with a frequency greater than the upper limit of human hearing, approximately 20 kHz. By penetrating soft tissue, and measuring the reflection signal, the ultrasound can reveal the structure of the tissue.
Medical sonography is an ultrasound-based diagnostic medical imaging technique used to visualize anatomical structures, such as muscles, tendons, and many other internal organs. The visualization reveals the size, shape, and pathological conditions of the structures. Ultrasound is also used to visualize a fetus during prenatal care.
Medical sonography is one of the most widely used diagnostic tools in modern medicine. The technology is relatively inexpensive and portable. As currently applied in the medical environment, ultrasound poses no known risks to the patient. Sonography is generally described as a safe test because it does not use ionizing radiation, which imposes hazards, such as cancer and chromosome breakage.
An ultrasonic signal is typically produced by a piezoelectric transducer encased in a probe. Strong, short electrical pulses from the ultrasound scanner make the transducer vibrate at the desired frequency. The frequencies can be anywhere between 2 and 15 MHz. The sound is focused either by the shape of the transducer, a lens in front of the transducer, or a complex set of control pulses from the ultrasound scanner. This focusing produces an arc-shaped sound wave from the face of the transducer. The wave travels into the body and comes into focus at a desired depth. Newer technology transducers use phased array techniques to enable the sonographic scanner to change the direction and depth of focus. Almost all piezoelectric transducers are made of ceramic. Materials on the face of the transducer enable the sound to be transmitted efficiently into the body. For example, a water-based gel is typically placed between the skin and the probe.
The sound wave is partially reflected from tissues having different densities. Specifically, sound is reflected anywhere there are density changes in the body, e.g. blood cells in blood plasma, small structures in organs, and other body fluids. Some of the reflections return to the transducer. The reflected sound vibrates the transducer, the transducer turns the vibrations into electrical pulses that travel to the ultrasonic scanner where the pulses are processed and transformed into an image.
It could be noted that sound wave is usually a short pulse with a specific carrier frequency. Moving objects change this frequency on reflection, so that the Doppler effect, which shifts the frequency, can be used. Therefore, the sonographic scanner operates as follows. The signals strength and length of time between transmitting and receiving the signal is measured. From this, the focal length for the phased array is deduced to enable rendering of an in-focus image of at a particular depth. The image can be in color.
Conventional ultrasound scanners display the images as thin, flat sections of the body. Advancements in ultrasound technology include three-dimensional (3-D) ultrasound, which formats the sound wave data into 3-D images. Four-dimensional (4-D) ultrasound is 3-D ultrasound with motion. Four different modes of ultrasound are used in medical imaging.                1. A-mode: A-mode is the simplest type of ultrasound. A single transducer scans a line through the body with the echoes plotted on a screen as a function of depth. Therapeutic ultrasound aimed at a specific tumor or calculus is also A-mode, to allow for pinpoint accurate focus of the destructive wave energy.        2. B-mode: In B-mode ultrasound, a linear array of transducers simultaneously scans a plane through the body that can be viewed as a two-dimensional image on screen.        3. M-mode: M stands for motion. In M-mode, a rapid sequence of B-mode scans, where images follow each other in sequence on screen, enable users to see and measure range of motion, as the organ boundaries that produce reflections move relative to the probe.        4. Doppler mode: This mode makes use of the Doppler effect.        
Doppler ultrasound is a special ultrasound technique that evaluates, e.g., blood flow in the major arteries, and veins in the abdomen, arms, legs and neck. There are three types of Doppler ultrasound.                1. Color Doppler uses a computer to convert Doppler measurements into an array of colors to visualize the speed and direction of blood flow through a blood vessel.        2. Power Doppler is a newer technique that is more sensitive than color Doppler and capable of providing greater detail of blood flow, especially in vessels that are located inside organs. Power Doppler, however, does not help the user to determine the direction of flow, which may be important in some situations.        3. Spectral Doppler displays blood flow measurements graphically, in terms of the distance traveled per unit of time, instead of displaying Doppler measurements visually.        
There are several advantages of ultrasound imaging. It images muscle and soft tissue well and is particularly useful for delineating the interfaces between solid and fluid-filled spaces. It can render images in real-time, where the user can dynamically select the most useful section for diagnosing and documenting changes, often enabling rapid diagnoses. It also shows the structure of organs.
As a disadvantage, sonography does not penetrate bone very well. Therefore, sonography of the brain is very limited. In addition, it performs very poorly when there is a gas between the transducer and the organ of interest, due to the extreme differences in sound impedance. For example, overlying gas in the gastrointestinal tract often makes ultrasound scanning of the pancreas difficult, and lung imaging is not possible, apart from demarcating pleural effusions. Even in the absence of bone or air, the depth penetration of ultrasound is limited, making it difficult to image structures deep in the body, especially in obese patients.
Directed Graphs
A graph G is an ordered pair G:=(V, E) that is subject to the following conditions.                1. V is a set, whose elements are called vertices or nodes; and        2. E is a set of edges connecting pairs of nodes.        
The vertices belonging to an edge are called the ends, endpoints, or end vertices of the edge. The order of a graph is |V|, i.e., the number of vertices. A graph's size is |E|, the number of edges. The degree of a vertex is the number of other vertices that are connected to the vertex by edges.
There are two broad categories of graphs: directed graphs (digraphs), and undirected graph. A directed graph or digraph G is an ordered pair G:=(V, A) where A is a set of ordered pairs of vertices, called directed edges. If there is an edge (v, w), then node w is adjacent to node v. A graph is a weighted graph if a positive number (weight) is assigned to each edge. Such weights can represent, for example, costs, lengths or capacities. The weight of the graph is the sum of the weight assigned to all edges. The weight of an edge in a directed graph is often thought of as its length. The length of a path <v0, v1, . . . , vn> is the sum of the lengths of all component edges <vi, vi+1>.
Breathing Cycle Estimation
U.S. Pat. No. 6,237,593 describes methods for estimating breathing (respiration) in continuous positive airway pressure (CPAP) treatment. The CPAP apparatus typically includes a flow generator for supplying air to a mask via a gas delivery tube. With changing air flow, the flow generator's speed and/or driving electrical current alters in a manner defined by the controlling circuitry. Signals can be derived from measurements of motor speed and current, and these signals vary cyclically with patient respiration. By filtering to reject non-respiratory components, the resultant signal can be utilized to determine the instants in time at which the patient starts to inhale and exhale. The filtered signal also can be linearized using a predetermined knowledge of the pressure/flow/speed characteristics of the flow generator, and thus to derive a volumetric measure of airflow.
Motto et al. describe a procedure for the automated estimation of the phase relation between thoracic and abdominal breathing signals measured by inductance plethysmography (RIP), Motto et al., “Automated estimation of the phase between thoracic and abdominal movement signals,” IEEE Transactions on Biomedical Engineering, Volume 52, Issue 4, Pages 614-621, April 2005. That estimation is performed using linear filters, binary converters and an exclusive-or gate. The filters are designed off-line from prior knowledge of the spectrum of subjects' respiration, reducing computational complexity and providing on-line processing capabilities. Some numerical results based on simulated time series and infant respiration data are provided, showing that the method is less biased than the Pearson correlation method, commonly used for assessment of thoraco-abdominal asynchrony.
Sarrut et al., describe a criteria incorporating spatiotemporal information to evaluate the accuracy of model-based methods capturing breathing motion from 4-DCT images, see Sarrut et al., “A Comparison Framework for Breathing Motion Estimation Methods From 4-D Imaging,” IEEE Transactions on Medial Imaging,
Volume 26, Issue 12, Pages 1636-1648, December 2007. That evaluation relies on the identification and tracking of landmarks in the 4-DCT images.
Radiotherapy
Radiotherapy attempts to direct high-energy ionizing radiation at tumors while sparing healthy tissue. One form of radiation therapy is particle beam therapy, where a depth of a maximum exposure can be controlled. However, the location of the tumors, especially tumors near organs, such that liver, lung, stomach and heart, can change significantly during the treatment as the diaphragm moves in and out. Therefore, it is desired to measure the change of location and shape of the tumor and organs so that the radiation beam can be appropriate controlled.
Radiotherapy uses ionizing radiation as part of cancer treatment to control malignant cells. It may be used for curative or adjuvant cancer treatment. It is used as palliative treatment, where a cure is not possible and the aim is for local disease control or symptomatic relief, or as therapeutic treatment, where the therapy has survival benefit and it can be curative. Radiotherapy is used for the treatment of malignant tumors, and may be used as the primary therapy. It is also common to combine radiotherapy with surgery, chemotherapy, hormone therapy or some combination of the three.
Radiation therapy is commonly applied primarily to the tumor. The radiation fields may also include adjacent lymph nodes if they are clinically involved with the tumor, of if there is thought to be a risk of sub-clinical malignant spread. It is necessary to include a margin of normal tissue around the tumor to allow for uncertainties in the set-up of the patient, and internal tumor motion.
It should be noted, that radiotherapy is typically provided over several weeks, e.g., three or four, to allow the patient to recover between treatments. Thus, identical set-ups are difficult to achieve. Therefore, the patient's skin is usually marked with indelible ink, during treatment planning, to indicate to the radio therapist technician how to set-up the patient relative to the treatment machine. A light beam, which is collocated with the radiation source, can be used to aim the beam and adjust the collimator during the set-up.
The uncertainties in the set-up can also be caused by internal movement, for example, respiration and bladder filling, and movement of external skin marks relative to the tumor location.
To spare normal tissues, such as skin or organs, which radiation must pass penetrated, in order to treat the tumor, shaped radiation beams are aimed from several angles of exposure to intersect at the tumor, providing a much larger absorbed at the tumor than in the surrounding, healthy tissue. Typically, the radiation source is placed on a gantry that rotates around the patient. The goal is to place the tumor at the center of the circle, so that the beam always passed the tumor, and much less frequently through healthy tissue.